Seismic surveying is used to perform characterization of subterranean elements in a subterranean structure. Examples of subterranean elements of interest include hydrocarbon-bearing reservoirs, fresh water aquifers, gas injection zones, and other subterranean elements. Seismic surveying is performed by deploying seismic sources (e.g., air guns, vibrators, explosives, etc.) and seismic receivers (e.g., hydrophones, geophones, etc.). The seismic sources are used to produce seismic waves (e.g., acoustic waves) that are propagated into the subterranean structure, with some of these seismic waves reflected from the subterranean elements of interest. The reflected seismic waves are received by the seismic receivers.
In a marine survey environment, survey hardware components (e.g., sources and receivers) can be towed through a body of water. An interesting characteristic of a seismic source is the seismic source's far-field signature. The signature of the seismic source refers to the shape of the signal transmitted by the seismic source. The signature of the seismic source varies with distance from the seismic source. Along a given direction, this signature varies with increasing distance from the seismic source, until at some given distance, the signature achieves a relatively stable shape. At greater distances than this given distance, the signature remains the same, but the amplitude decreases inversely proportional to the distance. The region where the signature shape does not change significantly with distance is known as the far field of the seismic source.
In many scenarios, it is difficult, if not impossible, to measure the far-field source signature in a direct way. For example, in the continental shelf, the water depth is insufficient to prevent the measurements from being substantially affected by sea-bottom reflections. Other practical obstacles also exist to perform true far-field measurements. A conventional technique of obtaining knowledge about far-field signatures is to estimate the far-field signatures based on near-field measurements, obtained normally by hydrophones mounted next to the seismic source elements. Alternatively, a far-field of a source can be estimated according to a model of the far-field signature based on measured physical parameters.
Conventional techniques for estimating the far-field signature can only provide a signature of limited time length. Conventionally, this time length is about 0.5 seconds, depending on tow speed, which is equivalent to the marine vessel speed relative to the water. The length is shorter when the towing speed is higher. Although the 0.5-second length is sufficient in many cases, it may not be sufficient in other cases.